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Aristarchus

A Mass is a Number

A Radius is a Number

A Name is an unbound Identifier

A Posn is a (posn Number Number)

Represents a coordinate pair.

Definitional Forms:

(body Name Mass Radius):

​ Binds a Name to an internal Structure containing the mass and radius.

ex: (body earth 5.972e+24 6.3781e+6)

ex: (body sun 1.989e+30 6.957e+8)

A Distance is a Number, represents the radius between the centers of two things

(connection Name Identifier Identifier Distance) :

​ Binds a Name to an internal Structure containing two identifiers and the distance between their centers.

ex: (connection earth-sun sun earth 1.496e+11)

(system Name (Connection ...)):

​ binds a Name to an internal Structure containing a list of connections

ex: (system Pluto-moons (pluto-charon pluto-hydra pluto-nix pluto-styx pluto-kerberos))

Expressions:

A Formula is one of :

  • surface-gravity
  • escape-velocity
  • kepler3-period
  • L1
  • L2
  • L3
  • L4
  • L5

A Mode is either 'answer or 'steps

'answer computes the answer to the formula with the given input.

'steps produces a webpage with step-by-step solutions.

An Expression is (Formula Structure ... [#:mode Mode])

(surface-gravity Body):

Finds the surface gravity of a body. The output is in m/s^2.

ex: (surface-gravity earth) -> ~9.79

(escape-velocity body)

Finds the escape velocity from a body. The output is in m/s

ex: (escape-velocity earth) -> ~11179.56

(kepler3-period connection)

Finds the period of an orbital system. The output is in s

ex: (kepler3-period earth-sun) -> ~31554700.48

31554700.4807 seconds is approximately 365.2164 days.

(L1 connection)

Finds the L1 lagrange point of an orbital system. The output is a posn.

ex: (L1 earth-sun) -> (posn 148103583760.57556 0)

(L2 connection)

Finds the L2 lagrange point of an orbital system. The output is a posn.

ex: (L2 earth-sun) -> (posn 151096416239.42444 0)

(L3 connection)

Finds the L3 lagrange point of an orbital system. The output is a posn.

ex: (L3 earth-sun) -> (posn -149600187156.13324 0)

(L4 connection)

Finds the L4 lagrange point of an orbital system. The output is a posn.

ex: (L4 earth-sun) -> (posn 74799550825.28027 129557400406.15201)

(L5 connection)

Finds the L5 lagrange point of an orbital system. The output is a posn.

ex: (L5 earth-sun) -> (posn 74799550825.28027 129557400406.15201)

For a derivation of Lagrange point calculations:

​ https://map.gsfc.nasa.gov/ContentMedia/lagrange.pdf

Formula:

An arg is an identifier.

An Association list is a [(identifier any) ...].

An MSE (Math-s-expression) is one of:

  • Identifier
  • Symbol
  • Number
  • String
  • (+ MSE MSE ...)
  • (- MSE MSE ...)
  • (* MSE MSE ...)
  • (/ MSE MSE)
  • (sqrt MSE)
  • (expt MSE MSE)
  • (posn MSE MSE)

(formula (Name arg ...) Association-List MSE)`

ex:

(formula (surface-gravity body)
         ((G G) (M_b (body-mass body)) (r (body-radius body)))
         (/ (* G M_b) (expt r 2))))